Lp-norm non-negative matrix factorization and its application to singing voice enhancement
Tomohiko Nakamura, Hirokazu Kameoka · 2015
Measures of sparsity are useful in many aspects of audio signal processing including speech enhancement, audio coding and singing voice enhancement, and the well-known method for these applications is non-negative matrix factorization (NMF), which decomposes a non-negative data matrix into two non-negative matrices. Although previous studies on NMF have focused on the sparsity of the two matrices, the sparsity of reconstruction errors between a data matrix and the two matrices is also important, since designing the sparsity is equivalent to assuming the nature of the errors. We propose a new NMF technique, which we called Lp-norm NMF, that minimizes the Lpnorm of the reconstruction errors, and derive a computationally efficient algorithm for Lp-norm NMF according to an auxiliary function principle. This algorithm can be generalized for the factorization of a real-valued matrix into the product of two real-valued matrices. We apply the algorithm to singing voice enhancement and show that adequately selecting p improves the enhancement.